Khan.scratchpad.disable(); To move up to the maestro level in his piano school, Christopher needs to master at least $137$ songs. Christopher has already mastered $32$ songs. If Christopher can master $2$ songs per month, what is the minimum number of months it will take him to move to the maestro level?
Solution: To solve this, let's set up an expression to show how many songs Christopher will have mastered after each month. Number of songs mastered $=$ $ $ Months at school $\times$ Songs mastered per month $+$ Songs already mastered Since Christopher Needs to have at least $137$ songs mastered to move to maestro level, we can set up an inequality to find the number of months needed. Number of songs mastered $\geq 137$ Months at school $\times$ Songs mastered per month $ +$ Songs already mastered $\geq 137$ We are solving for the months spent at school, so let the number of months be represented by the variable $x$ We can now plug in: $x \cdot 2 + 32 \geq 137$ $ x \cdot 2 \geq 137 - 32 $ $ x \cdot 2 \geq 105 $ $x \geq \dfrac{105}{2} \approx 52.50$ Since we only care about whole months that Christopher has spent working, we round $52.50$ up to $53$ Christopher must work for at least 53 months.